Cubic Interpolation (Interpolation, part II)

May 29, 2012

In a previous entry, we had a look at linear interpolation and concluded that we should prefer some kind of smooth interpolation, maybe a polynomial.

However, we must use a polynomial of sufficient degree so that neighboring patches do not exhibit very different slopes on either side of known points. This pretty much rules out quadratic polynomials, because polynomials of the form ax^2+bx+c are only capable of expressing (strictly) convex (or concave) patches. A quadratic piece-wise function would look something like:

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Wallpaper: Rust Matrix

May 27, 2012

(Rust Matrix, 1920×1200)

More wallpapers can be found here


Wallpaper: Stone Squid

May 27, 2012

(Stone Squid, 1920×1200)

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Wallpaper: Rocket to Mars

May 27, 2012

(Rocket To Mars, 1920×1200)

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Fast Fibonacci

May 22, 2012

The Fibonacci numbers are very interesting for many reasons, from seed heads to universal coding (such as Taboo Codes). Just figuring how to compute them efficiently is plenty of fun.

The classical formulation of the Fibonacci numbers is given by the following recurrence:

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Linear Interpolation (Interpolation, part I)

May 15, 2012

In a couple of different occasions I discussed the topic of interpolation, without really going into the details. Lately, I had to interpolate data and that got me interested (again) in interpolation; and I think I should share some of the things I learned.

In this first post (of a series), let us begin by the simplest interpolation of all (after constant interpolation): linear interpolation.

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Wallpaper: Self-Contained

May 12, 2012

(Self-Contained, 1920×1200)